//! R2-b: the cut-cell added-mass pin — the overset's instrument
//! (`overset_added_mass.rs`) rebuilt on embedded3.
//!
//! A no-slip circular cylinder of radius `R` translates through a closed
//! box of still fluid, `x_c(t) = A sin ωt`, on the periodic slab (nz cells).
//! The in-phase force is the added-mass reaction `F = −m_a ẍ` with
//! `m_a = ρ π R²` (unbounded potential flow) plus Stokes's viscous
//! correction `4 / √(π β)`, `β = R² ω / ν`, plus a small blockage term for
//! the box. The operator route's F_x is fitted to `c_s sin ωt + c_c cos ωt +
//! c_0` over the last two of `periods` periods: `C_m = c_s / (ρ π R² A ω²)`
//! (with `x_c = A sin ωt`, `−m_a ẍ = m_a A ω² sin ωt`), the viscous part
//! `c_c / (ρ π R² A ω²)` against `4 / √(π β)`.
//!
//! Knobs: `RTX_E3_AM_N` (64), `RTX_E3_AM_NZ` (4), `RTX_E3_AM_PERIODS` (4),
//! `RTX_E3_AM_SCHEME` (tvd | upwind), `RTX_E3_AM_CSV=<path>`.
use rtx_cfd::solvers::incompressible::ConvectionScheme;
use rtx_cfd::solvers::incompressible::embedded3::{
    Body, Boundaries, Field, Fluid, Grid, Parameters, Side, Solver, WallScheme,
};
use std::f64::consts::PI;
use std::io::Write as _;

const RHO: f64 = 1.0;
const NU: f64 = 5e-5;
const R: f64 = 0.1;
const CX: f64 = 0.5;
const CY: f64 = 0.5;
const AMP: f64 = 0.005;
const OMEGA: f64 = 2.0 * PI;

fn env_f(name: &str, default: f64) -> f64 {
    std::env::var(name)
        .ok()
        .and_then(|v| v.parse().ok())
        .unwrap_or(default)
}

/// Least squares of `y ≈ c_s sin ωt + c_c cos ωt + c_0`.
fn fit(samples: &[(f64, f64)]) -> (f64, f64, f64) {
    let mut m = [[0.0f64; 3]; 3];
    let mut rhs = [0.0f64; 3];
    for &(t, y) in samples {
        let b = [(OMEGA * t).sin(), (OMEGA * t).cos(), 1.0];
        for i in 0..3 {
            rhs[i] += b[i] * y;
            for j in 0..3 {
                m[i][j] += b[i] * b[j];
            }
        }
    }
    // Gaussian elimination with partial pivoting.
    let mut a = [[0.0f64; 4]; 3];
    for i in 0..3 {
        a[i][..3].copy_from_slice(&m[i]);
        a[i][3] = rhs[i];
    }
    for i in 0..3 {
        let piv = (i..3).max_by(|&p, &q| a[p][i].abs().total_cmp(&a[q][i].abs())).unwrap();
        a.swap(i, piv);
        for k in 0..3 {
            if k != i {
                let f = a[k][i] / a[i][i];
                for j in 0..4 {
                    a[k][j] -= f * a[i][j];
                }
            }
        }
    }
    (a[0][3] / a[0][0], a[1][3] / a[1][1], a[2][3] / a[2][2])
}

#[test]
#[ignore = "R2-b: the cut-cell added-mass pin (minutes per rung on the host)"]
fn cut_cell_added_mass() {
    let n = env_f("RTX_E3_AM_N", 64.0) as usize;
    let nz = env_f("RTX_E3_AM_NZ", 4.0) as usize;
    let periods = env_f("RTX_E3_AM_PERIODS", 4.0) as usize;
    let scheme = match std::env::var("RTX_E3_AM_SCHEME").as_deref() {
        Ok("upwind") => ConvectionScheme::Upwind,
        _ => ConvectionScheme::TvdVanAlbada,
    };
    let h = 1.0 / n as f64;
    let lz = nz as f64 * h;
    let period = 2.0 * PI / OMEGA;
    // The overset pin's step rule (its patch spacing = h here).
    let dt_raw = 0.4 * (h * h / (4.0 * NU)).min(h).min(0.2 * h / (AMP * OMEGA));
    let steps_per_period = (period / dt_raw).ceil() as usize;
    let dt = period / steps_per_period as f64;
    let beta = R * R * OMEGA / NU;
    let stokes = 4.0 / (PI * beta).sqrt();
    println!(
        "  cut-cell added mass: n = {n} (R/h {:.1}), nz {nz}, dt = {dt:.3e} ({steps_per_period} per period), A/R = {:.3}, KC = {:.3}, β = {beta:.0}: Stokes C_m ≈ {:.3} (viscous {:.3})",
        R / h,
        AMP / R,
        2.0 * PI * AMP / R,
        1.0 + stokes,
        stokes
    );
    let mut solver = Solver::new(
        Fluid {
            density: RHO,
            viscosity: RHO * NU,
            reference_velocity: AMP * OMEGA,
            reference_length: 2.0 * R,
        },
        Parameters {
            corrector_steps: 3,
            inner_stop_factor: 1e-3,
            tolerance: 1e-8,
            convection_scheme: scheme,
            wall_scheme: WallScheme::CutCell,
            boundaries: Boundaries {
                z0: Side::Periodic,
                z1: Side::Periodic,
                ..Boundaries::default()
            },
            max_surface_speed: Some(AMP * OMEGA * 1.05),
            ..Parameters::default()
        },
    );
    solver.set_boundary_velocity(|_, _, _, _| (0.0, 0.0, 0.0));
    let xc = |t: f64| CX + AMP * (OMEGA * t).sin();
    let uc = |t: f64| AMP * OMEGA * (OMEGA * t).cos();
    let body = Body::from_sdf(move |x, y, _z, t| ((x - xc(t)).powi(2) + (y - CY).powi(2)).sqrt() - R)
        .with_surface_velocity(move |_x, _y, _z, t| (uc(t), 0.0, 0.0));
    solver.set_moving_body(body);
    let g = Grid::cubic(n, n, nz, h);
    let mut field = Field::new(g);
    solver.initialize(&mut field);
    let mut csv = std::env::var("RTX_E3_AM_CSV").ok().map(|p| {
        let mut f = std::fs::File::create(p).expect("csv");
        writeln!(f, "t,xc,fx,fy,fx_rec,residual,fresh").unwrap();
        f
    });
    let mut samples: Vec<(f64, f64, f64)> = Vec::new();
    let mut worst = 0.0f64;
    let start = std::time::Instant::now();
    for step in 0..periods * steps_per_period {
        let r = solver.advance(&mut field, dt);
        let t = (step + 1) as f64 * dt;
        worst = worst.max(r.final_residual);
        assert!(r.final_residual.is_finite(), "death at step {step}");
        let mask = solver.mask().expect("mask");
        let body = solver.body().expect("body");
        let f = mask.cut_wall_force(body, &field, RHO * NU, t).expect("cut wall");
        let fr = mask
            .cut_wall_force_reconstructed(body, &field, RHO * NU, t, None)
            .expect("reconstructed");
        let (fx, fy, fx_rec) = (f[0] / lz, f[1] / lz, fr[0] / lz);
        samples.push((t, fx, fx_rec));
        if let Some(c) = csv.as_mut() {
            writeln!(c, "{t:.6},{:.6},{fx:.6e},{fy:.6e},{fx_rec:.6e},{:.3e},{}", xc(t), r.final_residual, r.fresh_cells).unwrap();
        }
        if (step + 1) % steps_per_period == 0 {
            println!(
                "    period {}: F_x at the end {fx:+.4e} (reconstructed {fx_rec:+.4e}), residual {:.1e}, {:.0} s",
                (step + 1) / steps_per_period,
                r.final_residual,
                start.elapsed().as_secs_f64()
            );
        }
    }
    let t0 = (periods as f64 - 2.0) * period - 1e-12;
    let scale = RHO * PI * R * R * AMP * OMEGA * OMEGA;
    let op: Vec<(f64, f64)> = samples.iter().filter(|s| s.0 > t0).map(|s| (s.0, s.1)).collect();
    let rec: Vec<(f64, f64)> = samples.iter().filter(|s| s.0 > t0).map(|s| (s.0, s.2)).collect();
    let (cs, cc, c0) = fit(&op);
    let (cs_r, cc_r, _) = fit(&rec);
    println!(
        "  ADDED MASS n = {n}: C_m operator {:.4} (reconstructed {:.4}) vs Stokes {:.3} unbounded / 1.135 confined (potential flow 1.071 in the unit box + 0.064); viscous {:.4} (reconstructed {:.4}) vs {:.3}; offset {:+.3e}; worst residual {worst:.1e}; {:.0} s",
        cs / scale,
        cs_r / scale,
        1.0 + stokes,
        cc / scale,
        cc_r / scale,
        stokes,
        c0,
        start.elapsed().as_secs_f64()
    );
}